Question

In what ratio does y axis divide the join of (-2,1) and (4,5)? Find the coordinates of the point of intersection

Answer 1

therefore
(X,Y) is (0,7/3)
hope this will help u

Answer 2

Ratio = 1:2

Point of intersection = $(0,\dfrac{7}{3})$

Explanation:

Equation of line passing through (a,b) and (c,d) =$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Then, Equation of line passing through (-2,1) and (4,5)=$(y-5)=\dfrac{5-1}{4-(-2)}(x-4)$

$(y-5)=\dfrac{4}{6}(x-4)$

$(y-5)=\dfrac{2}{3}(x-4)$

Put x=0

$(y-5)=\dfrac{2}{3}(0-4)$

$y-=\dfrac{-8}{3}+5=\dfrac{7}{3}$

⇒ $(0,\dfrac{7}{3})$ is the intersection point of line joining (-2,1) and (4,5) and y-axis.

Let the ratio be k:1.

Section formula : when a point P divides a line segment AB with endpoints A$(x_1,y_1)$ and B $(x_2,y_2)$ in m:n , then the coordinates of p is given by :-

$x=\dfrac{mx_2+nx_1}{m+n}\\\\ y=\dfrac{my_2+ny_2}{m+n}$

Then,

For given situation, we have

$0=\dfrac{k(4)+1(-2)}{k+1}\\\\\Rightarrow\ 4k-2=0\\\\\Rightarrow\ k=\dfrac{1}{2}$

$k:1=\dfrac{1}{2}:1\\\\=1:2$

Thus , the y axis divides the join of (-2,1) and (4,5) in ratio 1:2.

Learn more:

Find the coordinates of the point of intersection of the lines x+2y and 3x+4y=1​

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